Solve: Square Root of 16 Times 4 Squared Minus 3 Cubed

Order of Operations with Roots and Exponents

Solve:

16⋅42−33⋅1 \sqrt{16}\cdot4^2-3^3\cdot\sqrt{1}

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve:

16⋅42−33⋅1 \sqrt{16}\cdot4^2-3^3\cdot\sqrt{1}

2

Step-by-step solution

Begin by evaluating the square roots: 16=4 \sqrt{16} = 4 and 1=1 \sqrt{1} = 1 .

Substitute these back into the expression:

4⋅42−33⋅1 4\cdot4^2-3^3\cdot1

Calculate each term:

  • 42=16 4^2 = 16 , so 4⋅16=64 4\cdot16 = 64

  • 33=27 3^3 = 27 , so 27⋅1=27 27\cdot1 = 27

Subtract the second result from the first:

64−27=37 64 - 27 = 37

3

Final Answer

37

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Square roots and exponents first, then multiplication and subtraction
  • Technique: Calculate 16=4 \sqrt{16} = 4 , 42=16 4^2 = 16 , 33=27 3^3 = 27 separately
  • Check: Final calculation 4⋅16−27⋅1=64−27=37 4 \cdot 16 - 27 \cdot 1 = 64 - 27 = 37 ✓

Common Mistakes

Avoid these frequent errors
  • Working left to right without following PEMDAS
    Don't solve 16⋅42 \sqrt{16} \cdot 4^2 first then subtract = wrong order! This ignores that exponents and roots come before multiplication in order of operations. Always evaluate all roots and exponents first, then handle multiplication and subtraction.

Practice Quiz

Test your knowledge with interactive questions

What is the result of the following equation?

\( 36-4\div2 \)

FAQ

Everything you need to know about this question

Why do I calculate the square roots and exponents first?

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The order of operations (PEMDAS) tells us to handle exponents and roots before multiplication or subtraction. This ensures everyone gets the same answer!

What's the difference between 42 4^2 and 16 \sqrt{16} ?

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42 4^2 means 4 times 4 = 16, while 16 \sqrt{16} asks what number times itself equals 16? The answer is 4. They're inverse operations!

Do I need to know that 1=1 \sqrt{1} = 1 ?

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Yes! 1=1 \sqrt{1} = 1 because 1 × 1 = 1. It's one of the basic square roots you should memorize along with 4=2 \sqrt{4} = 2 , 9=3 \sqrt{9} = 3 , etc.

How do I remember 33 3^3 ?

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33 3^3 means 3 × 3 × 3. First: 3 × 3 = 9, then: 9 × 3 = 27. The small 3 tells you how many times to multiply!

Can I use a calculator for this?

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You can, but try doing it by hand first! Knowing perfect squares like 42=16 4^2 = 16 and cubes like 33=27 3^3 = 27 will make you much faster at math.

What if I get 64 - 27 wrong?

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Double-check your subtraction! 64 - 27: think 64 - 20 = 44, then 44 - 7 = 37. Or use: 60 - 27 = 33, then 33 + 4 = 37.

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